- (16 points) Assume that you toss a fair coin 5 times.

(a) (6 pts) What is the probability that you get 5 heads? (Show work and write the answer in simplest fraction form)

(b) (6 pts) What is the probability of getting heads in the 5^{th} toss, given that the first four tosses are tails? (Show work and write the answer in simplest fraction form)

(c) (4 pts) If event A is Getting heads in the 5^{th} toss and event B is The first four tosses are tails. Are event A and event B independent? Please explain.

- (8 points) A high school with 1000 students offers two foreign language courses : French and Japanese. There are 150 students in the French class roster, and 80 students in the Japanese class roster. We also know that 30 students enroll in both courses. Find the probability that a random selected student takes neither foreign language course. (Show work and write the answer in simplest fraction form)

- (12 points) Imagine you are in a game show. There are 5 prizes hidden on a game board with 20 spaces. One prize is worth $500, another is worth $200, and three are worth $50. You have to pay $50 to the host if your choice is not correct. Let the random variable x be the winning.

- (4 pts) Complete the following probability distribution. (Show the probability in fraction format and explain your work)

x | P(x) |

-$50 | |

$50 | |

$200 | |

$500 |

- (4 pts) What is your expected winning in this game? (Show work and round the answer to two decimal places)